Block #259,237

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/13/2013, 12:30:45 PM · Difficulty 9.9771 · 6,541,370 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

922ce60973fc096d02b9973c4a2ba4229ef252a91465e9cbc3bd4402050af334

View on Chainz ↗

Height

#259,237

Difficulty

9.977114

Transactions

Size

357 B

Version

Bits

09fa242b

Nonce

56,472

Timestamp

11/13/2013, 12:30:45 PM

Confirmations

6,541,370

Mined by

⛏️ P2SHANWrHiAp1jAKM5aGHVgFxnabiNY2WAv4pT

Merkle Root

417007ce90e2e982189f65010f1a283bbad7504a6292f9c4d3551263d90e140b

Transactions (2)

Coinbase588c8efb170d8a…07215a8f68eed0

1 in → 1 out10.0400 XPM109 B

ANWrHiAp…Y2WAv4pT

c35567ff07cb2f…994ce22e79350b

1 in → 1 out10.1700 XPM157 B

AbF7taLP…caPQgpyF

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

9.804 × 10⁹⁷(98-digit number)

98044063810774428896…59903802466012631041

Discovered Prime Numbers

p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin + 1

9.804 × 10⁹⁷(98-digit number)

98044063810774428896…59903802466012631041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.960 × 10⁹⁸(99-digit number)

19608812762154885779…19807604932025262081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.921 × 10⁹⁸(99-digit number)

39217625524309771558…39615209864050524161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.843 × 10⁹⁸(99-digit number)

78435251048619543117…79230419728101048321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.568 × 10⁹⁹(100-digit number)

15687050209723908623…58460839456202096641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.137 × 10⁹⁹(100-digit number)

31374100419447817246…16921678912404193281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.274 × 10⁹⁹(100-digit number)

62748200838895634493…33843357824808386561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.254 × 10¹⁰⁰(101-digit number)

12549640167779126898…67686715649616773121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.509 × 10¹⁰⁰(101-digit number)

25099280335558253797…35373431299233546241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.019 × 10¹⁰⁰(101-digit number)

50198560671116507595…70746862598467092481

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer